Answer:
A) The probability that each player gets an ace, a 2 and a 3 with the order unimportant = (72/1925) = 0.0374
B) The probability of winning the jackpot = (1/1200) = 0.0008333
Step-by-step explanation:
A) There are four Aces, four 2's, and four 3's, forming a set of 12 cards
These cards are to be divided at random between 4 players.
What is the probability that each player gets an ace, a 2 and a 3.
We start with the first player, the probability of these cards for the first player, with order not important (because order isn't important, there are 6 different arrangement of the 3 cards)
6 × (4/12) × (4/11) × (4/10) = (16/55)
Then the second player getting that same order of cards
6 × (3/9) × (3/8) × (3/7) = (9/28)
Third player
6 × (2/6) × (2/5) × (2/4) = (2/5)
Fourth player
6 × (1/3) × (1/2) × (1/1) = 1
Probability that each of the players get different cards is then a multiple of the probabilities obtained above
= (16/55) × (9/28) × (2/5) × 1
= (288/7700) = (72/1925) = 0.0374
B) The concluding part of the B question.
To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order). If you buy a ticket, what is your probability of winning the jackpot?
Probability of wimning the jackpot is a product the probability of getting the 3 white balls correctly (order unimportant) and the probability of picking the right red superball
Probability of picking 3 white balls from 10
First slot, any of the 3 lucky numbers can fill this slot, (3/10)
Second slot, only 2 remaining lucky numbers can fill this slot, (2/9)
Third slot, only 1 remaining lucky number can fill this slot, (1/8)
(3/10) × (2/9) × (1/8) = (1/120)
Probability of picking the right red superball
(1/10)
Probability of winning the jackpot = (1/120) × (1/10) = (1/120) × (1/10) = (1/1200) = 0.0008333
Hope this Helps!!!
